Re: Programming skills required by mathematicians?

In article <ddfb7$48688db5$82a1e228$25697@[EMAIL PROTECTED]
>,
Han de Bruijn  <Han.deBruijn@[EMAIL PROTECTED]
> wrote:
>Marshall wrote:

>> On Jun 25, 12:23 pm, hru...@[EMAIL PROTECTED]
 (Herman Rubin) wrote:

>>>In article
<fd0e8605-ee29-4365-a130-e0baedb3d...@[EMAIL PROTECTED]
>,
>>>translogi  <wilem...@[EMAIL PROTECTED]
> wrote:


	
[...]
>>>Computers are essentially a fixed program, the
>>>hardware, which then has a small initialized amount
>>>of software, quite variable, which enables it to
>>>try to do what the user wants.  Keep this in mind;
>>>understand what the hardware can do, which is
>>>different on different machines, and think in those
>>>terms, not the current poorly designed languages.

>> Not quite sure what you're saying here. If it's a
>> warning against basic, then sure. But thinking
>> in terms of specific machine architecture? That's
>> virtually never a good idea. Even if you're using
>> something antique like plain C, you're still a lot
>> better off than you are with assembly or machine
>> language. What is "the current poorly designed
>> languages" supposed to refer to?

>Knowing Herman Rubin a little bit, I just think he feels a bit slippery
>here, though he won't admit. H.R. isn't much of a computer minded person
>and he'd rather formulate his theoretical considerations on the backside
>of an envelope, hand written, I suppose. (Not that I have any objections
>against formulas written by hand ..)

I have programmed in Fortran, C, and assembler for 
different machines.  I am quite aware of even the
fact that efficiency for subroutines requires taking
into account the differences in the different machines,
and I have also stated that I can see how to produce
a somewhat high level assembler language easy to use.

Those who think HLLs are such a great idea, here is a
challenge.  The function I am giving arises naturally,
and it is quite difficult to do EFFICIENTLY in any HLL.

Let x be a positive real number, whose binary expansion
is x = \sum a_i/2^i, a_i = 0 or 1.  Then 

	f(x) = \sum i*a_i/2^i.

I have done some work on methods of generating non-uniform
random variables from uniform bits.  There are some technical
re****ts available from the Purdue Statistics Department.
Among them are some I call "infinite precision", in that
no computer roundoff is involved.  The easiest one of these
is to generate the density 2x from 0 to 1.  The entire
algorithm is

	I = distance to the first 1 in a random bit stream;
discard this part of the bit stream
	X = U with the I-th bit after the binary point
changed to 1.

Alas, few of these are efficient, except possibly on an FPGA,
but the amount of work is finite random for all distributions
in any number of dimensions with lower semi-continuous density.

I have a recent paper with Brad Johnson on acceptance-replacement
generation of exponential and normal random variables, using 
exponentials to test and reuse of successful test exponentials.
These vectorize or parallelize well if one changes the "control"
part of the algorithm somewhat, and that consideration also went
into the design of the algorithm.

I do know something about getting the power of the machine, and
doing operations beyond the low precision hardware.  Even if only
partial, there should be a convenient way of including assembler
instructions in a program without losing "optimization"; I have
done that on the CYBER 205.  I have also in my files a design for
a decent quick assembler for the 780; I cannot find what I did
on the 205, but I remember some of it, including the most complicated
single one.

One danger of HLLs is that the user has no idea of how long
something will take.  As for gotos, I find them easy to use,
and spaghetti code is best for spaghetti algorithms.

>Han de Bruijn



-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
         Phone: (765)494-6054   FAX: (765)494-0558